Chapter-8. Application of Integrals

The area bounded by the y-axis, y = cos x and y = sin x when 

A. 

B. 

C. 

D. 

The area of the circle x² + y² = 16 exterior to the parabola y² = 6x is

A. 

B. 

C. 

D. 

The area bounded by the curve, x-axis and the ordinates x = –1 and x = 1 is given by

A. 0

B. 

C. 

D. 

Find the area of the region 

Using the method of integration find the area of the region bounded by lines:

2x + y = 4, 3x - 2y = 6 and x - 3y + 5 = 0

Find the area bounded by curves 

Using the method of integration find the area bounded by the curve 

Find the area of the region enclosed by the parabola x² = y, the line y = x + 2 and x-axis

Find the area of the smaller region bounded by the ellipse  and the line 

Find the area of the smaller region bounded by the ellipse and the line 

Find the area enclosed by the parabola 4y = 3x² and the line 2y = 3x + 12

Find the area enclosed between the parabola y² = 4ax and the line y = mx

Find the area bounded by the curve y = sin x between x = 0 and x = 2π

Sketch the graph of and evaluate

Find the area of the region lying in the first quadrant and bounded by y = 4x², x = 0, y = 1 and y = 4

Find the area between the curves y = x and y = x²

Find the area under the given curves and given lines:

(i) y = x², x = 1, x = 2 and x-axis

(ii) y = x⁴, x = 1, x = 5 and x -axis

Area lying between the curve y² = 4x and y = 2x is

A. 

B. 

C. 

D. 

Smaller area enclosed by the circle x² + y² = 4 and the line x + y = 2 is

A. 2 (π - 2)

B. π - 2

C. 2π - 1

D. 2 (π + 2)

Using integration find the area of the triangular region whose sides have the equations y = 2x +1, y = 3x + 1 and x = 4.

Using integration finds the area of the region bounded by the triangle whose vertices are (-1, 0), (1, 3) and (3, 2).

Find the area of the region bounded by the curves y = x² + 2, y = x, x = 0 and x = 3

Find the area of the circle 4x² + 4y² = 9 which is interior to the parabola x² = 4y

Area of the region bounded by the curve y² = 4x, y-axis and the line y = 3 is

A. 2

B. 

C. 

D. 

Area lying in the first quadrant and bounded by the circle x² + y² = 4 and the lines x = 0 and x = 2 is

A. π

B. 

C. 

D. 

Find the area of the region bounded by the curve y² = 4x and the line x = 3

Find the area bounded by the curve x² = 4y and the line x = 4y - 2

Find the area of the region bounded by the parabola y = x² and 

The area between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a

Find the area of the smaller part of the circle x² + y² = a² cut off by the line 

Find the area of the region in the first quadrant enclosed by x-axis, line and the circle 

Find the area of the region bounded by the ellipse 

Find the area of the region bounded by the ellipse 

Find the area of the region bounded by x² = 4y, y = 2, y = 4 and the y-axis in the first quadrant.

Find the area of the region bounded by y² = 9x, x = 2, x = 4 and the x-axis in the first quadrant.

Find the area of the region bounded by the curve y² = x and the lines x = 1, x = 4 and the x-axis.